The Asymptotic Dynamics of de Sitter Gravity in three Dimensions

We show that the asymptotic dynamics of three-dimensional gravity with positive cosmological constant is described by Euclidean Liouville theory. This provides an explicit example of a correspondence between de Sitter gravity and conformal field theories. In the case at hand, this correspondence is established by formulating Einstein gravity with positive cosmological constant in three dimensions as an SL(2,C) Chern-Simons theory. The de Sitter boundary conditions on the connection are divided into two parts. The first part reduces the CS action to a nonchiral SL(2,C) WZNW model, whereas the second provides the constraints for a further reduction to Liouville theory, which lives on the past boundary of dS_3.